Implicit scaling of linear least squares problems

BIT Numerical Mathematics

Volumn 40, Issue 1, 2000, Pages 146-157

  Reid, J K ^a  

^a JKR Associates   (United Kingdom)

Author keywords

Backward errors; Iterative refinement; Qr factorization; Weighted linear least squares

Indexed keywords

EID: 0012031765     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022374520140     Document Type: Article

References (16)

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3. Å. Björck, Numerical Methods for Least Squares Problems, SIAM, Philadelphia, 1996.
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6. A. J. Cox and N. J. Higham, Stability of Householder QR factorization for weighted least squares problems, in Numerical Analysis 1997, Proceedings of the 17th Dundee Biennial Conference, D. F. Griffiths, D. J. Higham, and G. A. Watson, eds., Pitman Research Notes in Mathematics, 380, 1998, pp. 57-73.
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11. M. Gulliksson and P.-Å. Wedin, Modifying the QR-decomposition to constrained and weighted linear least squares, SIAM J. Matrix Anal. Appl. 13 (1992), pp. 1298-1313.
12. A. S. Householder, Unitary triangularization of a nonsymmetric matrix, J. ACM, 5 (1958), pp. 339-342.
13. M. J. D. Powell and J. K. Reid, On applying Householder transformations to linear least squares problems, Report TP 322, Theoretical Physics Division, Harwell Laboratory, 1968. Reproduced as an appendix to the report of Reid [15].
14. M. J. D. Powell and J. K. Reid, On applying Householder transformations to linear least squares problems, in Information Processing 68, A. J. H. Morrell, ed., North-Holland, Amsterdam, 1969, pp. 122-126.
15. J. K. Reid, Implicit scaling of linear least squares problems, Report RAL-TR-98-027, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, 1997.
16. G. W. Stewart, On the weighting method for least squares problems with linear equality constraints, BIT, 34 (1997), pp. 961-967.